Experiments and Crystal Plasticity Simulations on Plastic Anisotropy of Naturally Aged and Annealed Al–Mg–Si Alloy Sheets

The influence of the heat treatment on the plastic anisotropy of an Al–Mg–Si sheet was investigated by experiments and crystal plasticity simulations. Uniaxial tension tests were conducted for the naturally aged (T4 temper) and annealed (O temper) Al–Mg–Si sheets. Solute atoms Mg and Si form clusters in the T4 temper sheet, while they bind to form precipitates in the O temper sheet. It is found that the in-plane variation of the R value, texture, and grain size are almost identical for both sheets. By contrast, the anisotropy of the flow stress is clearly dissimilar; the flow stress is the highest in the diagonal direction for the O temper sheet, whereas the flow stress in that direction is nearly lowest for the T4 temper sheet. Thus, the heat treatment alters the anisotropy of the flow stress. The plastic behaviors of the specimens were simulated using the dislocation density-based crystal plasticity model. The influence of the dislocation interaction matrix on the plastic anisotropy was examined. The orientation dependence of the flow stress is found to be sensitive to the interaction matrix. The flow stresses predicted by the interaction matrix determined based on the dislocation dynamic simulation agree with the experimental results for the O temper sheet. Whereas this interaction matrix does not reproduce the flow stress anisotropy for the T4 temper sheet. When the interactions among the dislocations are set to equivalent—i.e., the interaction matrix is filled with unity—the crystal plasticity simulation results in the flow stress anisotropy that is similar to the experimental trend of the T4 temper sheet. In contrast to the flow stress, the R value is insensitive to the interaction matrix, and the predicted R values agree with the experimental results for both specimens.

Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

In this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion [10] which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation [37]. From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. [32] –which investigated materials with yielding described by the orthotropic criterion of Hill [19]– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s−1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations

Criterion for the occurrence of the macro destruction and formation of breaking during metal deformation

When generalizing the geometrically nonlinear law of Murnaghan elasticity to plasticity, a formally mathematical criterion was introduced for deformational macrofracture (macrocrack appearance) associated with an increase in elastic and plastic anisotropy as a failure cause. The use of the double potentiality of the governing equations in stresses and their velocities made it possible to obtain the reliable information on the structure of the deviatory section of the yield surface, the existence of which is a classical hypothesis in solid mechanics. The normal vector to the surface of the deviatory section is selected from two mutually orthogonal eigenvectors of the constructed operator. There are two families of regular concave surfaces, and a section surface is formed by joining the parts of two representatives of the families at singular points. To select normal vectors, the obtained ratio for them is used for isotropy. In connection with the considered problem of a double simple shift, it is established that multiple eigenvalues appear for the both normal vectors. To unambiguously determine the normal vector at a regular point, it is necessary to exclude the presence of multiple eigenvalues for the both normal vectors at the same time. At a singular point, the appearance of a multiple eigenvalue of one of the normal vectors is still unacceptable. These two conditions are necessary and sufficient to validate the governing equations of the generalized Murnaghan model. Otherwise, a macrocrack occurs. The theoretical construction is supported by the developed software complexes.

On the Use of Homogeneous Polynomial Yield Functions in Sheet Metal Forming Analysis

Sheet metal forming techniques are a major class of stamping and manufacturing processes of numerous parts such as doors, hoods, and fenders in the automotive and related supplier industries. Due to series of rolling processes employed in the sheet production phase, automotive sheet metals, typically, exhibit a significant variation in the mechanical properties especially in strength and an accurate description of their so-called plastic anisotropy and deformation behaviors are essential in the stamping process and methods engineering studies. One key gradient of any engineering plasticity modeling is to use an anisotropic yield criterion to be employed in an industrial content. In literature, several orthotropic yield functions have been proposed for these objectives and usually contain complex and nonlinear formulations leading to several difficulties in obtaining positive and convex functions. In recent years, homogenous polynomial type yield functions have taken a special attention due to their simple, flexible, and generalizable structure. Furthermore, the calculation of their first and second derivatives are quite straightforward, and this provides an important advantage in the implementation of these models into a finite element (FE) software. Therefore, this study focuses on the plasticity descriptions of homogeneous second, fourth and sixth order polynomials and the FE implementation of these yield functions. Finally, their performance in FE simulation of sheet metal cup drawing processes are presented in detail.

Effects of yield point and plastic anisotropy on results of elastic-plastic finite element analysis of tension leveling

Tension leveling is an important industrial process to eliminate the flatness defects and residual stresses of metal strips to provide high-quality sheet metals for subsequent sheet metal forming. The finite element (FE) method can be applied to elucidate the effects of process parameters on the quality of sheets after tension leveling for various materials. In our previous investigation, an accurate FE model considering the anisotropy and cyclic plasticity of materials has been established for the elastic-plastic FE analysis of tension leveling. In this study, we further studied the effects of the yield point and plastic anisotropy on tension leveling using the FE model established in our previous investigation. Aiming at improving the accuracy of simulation, a modified constitutive model was developed to describe the anisotropic hardening of materials under cyclic loading. The modified constitutive model was implemented into Abaqus/Standard as a user-defined material (UMAT) subroutine to simulate the development of the anisotropy in materials during tension leveling. The modified model was also applied to the FE analysis of sheet metal forming processes to demonstrate its simulation capability and accuracy.